Question

Determina el polinomio de grado 1 p (× ) si sabemos que p (1) =1y p (2) sea 1

Answer 1

  La forma general del polinomio es:  
                                                           p(x) = ax + b
 
                                         p(1) = 1 ⇒ p(1) = a(1) + b = 1              (1)
                                         p(2) = 1 ⇒ p(2) = a(2) + b = 1              (2)

         El sistema queda            a + b = 1                   (1)
                                               2a + b = 1                   (2)
                       La solución del sistema es a=0 y b=1
                     Por lo tanto el polinomio se queda p(x) = ax+b
                                                                             p(x) = 0x+1
                                                                             p(x) = 1